The Pressure Limitations on Flux Pile-up Reconnection

The problem of the plasma pressure limitations on the rapidity of flux pile-up magnetic reconnection is re-examined, following the claim made by Jardine and Allen (1998) that the limitations can be removed by relaxing the assumption of zero-vorticity two-dimensional plasma flows. It is shown that for a two-dimensional stagnation point flow with nonzero vorticity the magnetic merging rate cannot exceed the Sweet–Parker scaling in a low-beta plasma. The pressure limitation appears to be much less restrictive for weak three-dimensional flux pile-up, provided the perturbation length scale in the third dimension is much less than the global length scale. The actual reconnection rate in the latter case, however, is much lower than this upper estimate unless the current sheet width is also much less than the global scale.